Table 1: Equilibrium parameters of different simulated jet models along with solutions of the dispersion relation (23), corresponding to fastest growing first reflection mode, taken as input parameters for numerical simulations. The meaning of the symbols is as follows: $\gamma$ : jet flow Lorentz factor; $\varepsilon$ : specific internal energy; $c_{\rm s}$ : sound speed; p: pressure; $\nu$ : jet-to-ambient relativistic rest mass density contrast; $\eta$ : jet-to-ambient enthalpy contrast; $M_{\rm j}$ : internal jet Mach number; $k_{\parallel , \perp }$ : longitudinal/transverse wavenumbers; $\omega _{r,i}$ : real/imaginary part of the wave frequency. Labels aand j refer to ambient medium and jet, respectively. The primes are used to assign wavenumber and complex frequency in the reference frame comoving with jet. The last column shows the linear growth rate of KH instability in the jet reference frame expressed in dynamical time units, i.e. in which time is scaled to $R_{\rm j}/c_{\rm sj}$ . All the quantities in the table, except the last column, are expressed in units of the ambient density, $\rho _{\rm0a}$ , the speed of light, c, and the jet radius, $R_{\rm j}$ .
${\rm Model}$ $\gamma$ $\varepsilon_{\rm j}$ $\varepsilon_{\rm a}$ $c_{\rm sj}$ c_sa p $\nu$ $\eta$ $M_{\rm j}$ $k_{\parallel}$ $\omega_r$ $\omega_i$ ${k'_\parallel}$ $\omega'_{r}$ $\omega'_i$ $k_{{\rm j}\perp}$ $k_{\rm a\perp}$ ${\omega'}^{\rm dyn}_i$

A05 5 0.08 0.008 0.18 0.059 0.0027 0.11 0.11 5.47 0.30 0.20 0.026 1.32 7.20 0.13 7.08 0.53 0.73

B05 5 0.42 0.042 0.35 0.133 0.014 0.14 0.15 2.83 0.69 0.49 0.055 2.62 7.32 0.28 6.84 1.08 0.79

C05 5 6.14 0.614 0.55 0.387 0.205 0.44 0.51 1.80 2.00 1.60 0.114 5.73 9.98 0.57 8.17 1.07 1.05

D05 5 60.0 6.000 0.57 0.544 2.000 0.87 0.90 1.71 2.63 2.18 0.132 7.02 11.56 0.66 9.18 0.24 1.15

B10 10 0.42 0.042 0.35 0.133 0.014 0.14 0.15 2.88 0.50 0.41 0.031 3.59 10.28 0.31 9.64 0.94 0.90

C10 10 6.14 0.614 0.55 0.387 0.205 0.44 0.51 1.83 1.91 1.72 0.055 9.77 17.67 0.55 14.72 1.49 1.01

D10 10 60.0 6.000 0.57 0.544 2.000 0.87 0.90 1.73 2.00 1.81 0.063 9.67 16.58 0.63 13.47 0.20 1.10

B20 20 0.42 0.042 0.35 0.133 0.014 0.14 0.15 2.89 0.46 0.39 0.014 6.51 18.76 0.28 17.60 0.90 0.81

C20 20 6.14 0.614 0.55 0.387 0.205 0.44 0.51 1.83 1.44 1.37 0.027 13.89 25.38 0.54 21.24 1.28 0.99

D20 20 60.0 6.000 0.57 0.544 2.000 0.87 0.90 1.74 2.00 1.91 0.029 18.11 31.43 0.58 25.68 0.31 1.01

**Table 1:** Equilibrium parameters of different simulated jet models along with solutions of the dispersion relation (23), corresponding to fastest growing first reflection mode, taken as input parameters for numerical simulations. The meaning of the symbols is as follows: $\gamma$ : jet flow Lorentz factor; $\varepsilon$ : specific internal energy; $c_{\rm s}$ : sound speed; p: pressure; $\nu$ : jet-to-ambient relativistic rest mass density contrast; $\eta$ : jet-to-ambient enthalpy contrast; $M_{\rm j}$ : internal jet Mach number; $k_{\parallel , \perp }$ : longitudinal/transverse wavenumbers; $\omega _{r,i}$ : real/imaginary part of the wave frequency. Labels aand j refer to ambient medium and jet, respectively. The primes are used to assign wavenumber and complex frequency in the reference frame comoving with jet. The last column shows the linear growth rate of KH instability in the jet reference frame expressed in dynamical time units, i.e. in which time is scaled to $R_{\rm j}/c_{\rm sj}$ . All the quantities in the table, except the last column, are expressed in units of the ambient density, $\rho _{\rm0a}$ , the speed of light, c, and the jet radius, $R_{\rm j}$ .
${\rm Model}$	$\gamma$	$\varepsilon_{\rm j}$	$\varepsilon_{\rm a}$	$c_{\rm sj}$	c_sa	p	$\nu$	$\eta$	$M_{\rm j}$	$k_{\parallel}$	$\omega_r$	$\omega_i$	${k'_\parallel}$	$\omega'_{r}$	$\omega'_i$	$k_{{\rm j}\perp}$	$k_{\rm a\perp}$	${\omega'}^{\rm dyn}_i$
A05	5	0.08	0.008	0.18	0.059	0.0027	0.11	0.11	5.47	0.30	0.20	0.026	1.32	7.20	0.13	7.08	0.53	0.73
B05	5	0.42	0.042	0.35	0.133	0.014	0.14	0.15	2.83	0.69	0.49	0.055	2.62	7.32	0.28	6.84	1.08	0.79
C05	5	6.14	0.614	0.55	0.387	0.205	0.44	0.51	1.80	2.00	1.60	0.114	5.73	9.98	0.57	8.17	1.07	1.05
D05	5	60.0	6.000	0.57	0.544	2.000	0.87	0.90	1.71	2.63	2.18	0.132	7.02	11.56	0.66	9.18	0.24	1.15
B10	10	0.42	0.042	0.35	0.133	0.014	0.14	0.15	2.88	0.50	0.41	0.031	3.59	10.28	0.31	9.64	0.94	0.90
C10	10	6.14	0.614	0.55	0.387	0.205	0.44	0.51	1.83	1.91	1.72	0.055	9.77	17.67	0.55	14.72	1.49	1.01
D10	10	60.0	6.000	0.57	0.544	2.000	0.87	0.90	1.73	2.00	1.81	0.063	9.67	16.58	0.63	13.47	0.20	1.10
B20	20	0.42	0.042	0.35	0.133	0.014	0.14	0.15	2.89	0.46	0.39	0.014	6.51	18.76	0.28	17.60	0.90	0.81
C20	20	6.14	0.614	0.55	0.387	0.205	0.44	0.51	1.83	1.44	1.37	0.027	13.89	25.38	0.54	21.24	1.28	0.99
D20	20	60.0	6.000	0.57	0.544	2.000	0.87	0.90	1.74	2.00	1.91	0.029	18.11	31.43	0.58	25.68	0.31	1.01

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